1. Preheat the oven to 230°C with the rack in the middle position. Pat the chicken dry with paper towels. Sprinkle kosher salt liberally (about 2 teaspoons) on both sides of the chicken pieces.
2. Heat a 12-inch oven-safe heavy bottomed skillet over medium high heat. When the pan is hot, swirl in the ghee.
3. Add the chicken pieces skin-side down in the hot pan. Sear, undisturbed, until nicely browned and crispy, about 4 to 6 minutes. While the skin is crisping, add some freshly ground black pepper to the meaty side.
4. When the skin is golden brown, flip the pieces over and cook for 2 minutes more. Then, transfer the chicken to a platter.
5. Turn the heat off and add the shallots to the empty pan. Cook, stirring occasionally, until slightly softened, about 1 minute.
6. Turn the heat to medium and toss in the courgette and a sprinkle of salt. Sauté, stirring occasionally, until the courgette is lightly browned and tender, about 3 to 5 minutes.
7. Stir in the cherry tomatoes and garlic cloves. Cook until garlic is fragrant and some of the tomatoes have burst, about 1 minute.
8. Pour in the broth and balsamic vinegar and stir well to combine. Add the thyme sprigs.
9. Bring to a simmer and taste and adjust sauce for seasoning with more salt if needed.
10. Tuck in the chicken pieces, skin-side up, making sure the skin stays above the broth.
11. Transfer the pan to the hot oven and roast the chicken for 15-20 minutes. The dish is ready when the chicken juices run clear and the vegetables have softened into a chunky sauce.
12. Remove the skillet from the oven. Discard the thyme sprigs and garnish with fresh basil. Serve immediately.